We remark that this abstract formulation captures several standard gambling problems as special instances; see Table REF .
For example, if \(\mathcal {M}=\lbrace 2{\mathbf {e}}_1,2{\mathbf {e}}_2\rbrace \) , it corresponds to the standard (fair) coin betting game.
If \(\mathcal {M}=\lbrace o_1{\mathbf {e}}_1,\ldots ,o_K{\mathbf {e}}_K\rbrace \)  for some \(o_1,\ldots ,o_K>0\) , then the game becomes the horse race with odds \(o_1,\ldots ,o_K\) .
The most general case is when \(\mathcal {M}=\mathbb {R}_{>0}^K\) , where the game is typically known as the portfolio optimization in a stock market.
The continuous coin betting problem that corresponds to \(\mathcal {M}=\lbrace [2\widetilde{c},2(1-\widetilde{c})]\mathchoice{\colon }{\colon }{:{1mu}}{:}\widetilde{c}\in [0,1]\rbrace \)  was considered by [1]} to translate the idea of universal coin betting to the domain of online linear optimization.
